Radial Dependence of the Vertical Scale Height
in NGC 4565

S. Ryland Ely

2002 June 3

Abstract

NGC 4565, an edge-on spiral galaxy, was observed in the I band to determine the vertical scale height at several radii. The results were compared to van der Kruit and Searle's 1981 results. While the vertical brightness profiles obtained here strongly resemble those historical results, no conclusion could be made concerning the relationship of the vertical scale height and radius.

1. Introduction

Since a complete model of galactic structure should be independent of orientation, the extreme cases of edge-on and face-on galaxies provide important observations from very different vantage points. It is a natural first step to seek a model of the light distribution in these galaxies. Succeeding studies of the horizontal luminosity distribution in edge-on galaxies, van der Kruit and Searle (1981) showed that the vertical distribution of light is proportional to
C(r) sech²(z/z₀), where C(r) is a function of the radius, z is the height above the galactic midplane, and z₀is a constant known as the vertical scale height. Furthermore, van der Kruit and Searle found that the vertical scale height remains constant over the entire radius.

One of van der Kruit and Searle's targets, NGC 4565, has been chosen for this project because it is a prototypical edge-on spiral galaxy. Located in Coma Berenices, the galaxy has an inclination of 86^o. It is relatively large and bright and well-positioned in the sky for spring observing with the Great Ohio Telescope (GOT). The goal of this research was to examine the vertical brightness profiles of the target and attempt to rediscover van der Kruit and Searle's results, which are displayed in Fig. 1.

Figure 1. van der Kruit and Searle's 1981 results.

2. Observations

NGC 4565 was observed on 2002 May 5 UT through the 0.25 meter Great Ohio Telescope and its ST-8 CCD detector at -15 deg C. Nine evening flats were taken at exposure times from 10 to 55 seconds in V, I, and R filters. The V and R filters were used for other research by another PI carried out the same night. Seven zeros (actually 0.11-second exposures) were recorded next, followed by 12 darks: 5 x 30 s, 5 x 120 s, and 2 x 600 s. Only the 600 s darks were used for this project. Another 600 s was taken later in the evening as time allowed. At this point, the sky had become cloudy, and no more data was taken for about two hours while we waited for the sky to clear. The target, NGC 4565, was observed in I band in 6 x 600 s exposures as it moved from 1.3 to 1.6 airmasses. The center of the galaxy was positioned off the edge of the frame because the necessity of having a guide star within the guiding frame of the CCD limited the possible orientations of the exposures. The initial exposures were taken through about one magnitude of clouds, and the sky gradually cleared throughout the exposure time. Nine morning flats were taken, again in V, I, and R filters.

3. Reductions

Image reduction was carried out using IRAF. The seven zeros were combined and visually inspected. The three 600 s darks were combined and then zero-corrected using the combined zero. The results were used to dark- and zero-correct the flat fields and object frames. Visual inspection of the object frames showed them to be much less noisy, but retaining a bright ring characteristic of the GOT optics. After combining the flats, the object frames were flat-corrected. Although the resulting images were improved, a less noticeable darker ring replaced the bright ring of the uncorrected frames, implying that the IRAF task overcompensated for the optics. Because this problem seems unique among GOT users to date, it is supposed that the error is related to the long exposure times of the target. This completes basic data reduction.

Figure 2. (373 x 305 arcsec) One of six exposures after dark-, zero-, and flat-correcting. The necessity of having a guide star within the guiding field of the CCD required the center of the galaxy to be off the edge of the frame.

The next step was to remove cosmic rays from the images. This was simply a trial-and-error modification of the xzap task parameters to maximize removal of cosmic rays and other anomalies. while minimizing damage to the statistical distribution of photon counts. The parameters used were a 6-sigma threshold and a box size of 10.

Because no blank sky frames were taken, only a simple sky subtraction could be performed. This was carried out by finding in each object frame totally blank regions of the sky. Because of the problem with flat corrections, two regions with approximately the same sky brightness as the sky near the galaxy were chosen, their mean brightnesses were averaged, and the result was subtracted from the object frames. This means that the average background brightness (sources excluded) in some regions of each frame was somewhat positive, while in others it was somewhat negative, so that in the vicinity of the galaxy it is assumed to be zero.

The final stage in reduction was the registration and co-addition of the object frames. A reference frame was chosen and six stars were identified in each of the frames. The xregister task was used to register the images, and the overlap region was noted. All six object frames were then co-added and trimmed. The non-constant sky brightness was noted to be amplified in the co-added image.

Figure 3. (347 x 281 arcsec) Contour map of the co-added image. Note the imperfect flat-fielding as well as several stars within the galaxy's vicinity.

4. Results

Before results could be obtained, the final, co-added image must be rotated. This involved yet another trial-and-error method of rotating and checking the contour profiles until the plane of the galaxy seemed parallel to the x-axis. The next step was to find the centerline of the galaxy, which does not divide the image into two equal halves because the galaxy is not exactly edge-on. Vertical brightness profiles were examine at even intervals along the radius, and the midpoint of each was localized. The results were consistent beyond a certain radius, while within that radius the difference was within a few percent, so the midplane of the galaxy could be defined.

Figure 4. (424 x 175 arcsec) Completely reduced and rotated image from which data were taken. The blur in the upper left represents an area outside of the CCD detecting window. The midplane of the galaxy is horizontal with the page. Measurements were taken from the area below the midplane.

For measuring, it was decided to use the broader side of the galaxy because this allowed a larger range of measurements. The radius was divided into ten evenly-spaced, disjoint segments of width 20 pixels (14 arcsec) separated by 30 pixels. At each radius, measurements of the mean value and standard deviation were taken of several bins using the IRAF keyword imstat. Bin sizes were chosen according to two rules: the minimum bin size was 40 pixels (20 x 2); and, the relative error in each bin must be less than 15% (corresponding to a signal-to-noise ratio of about 7). When the mean pixel value was less than zero, or when the desired precision could not be obtained, that vertical height was considered the cut-off for that radius.

After obtaining these for four to twelve bins at each of ten radii, the photon counts were converted to an uncalibrated magnitude. This was done by converting the mean counts-per-pixel value to a mean counts-per-arcsecond value (using 0.49 arcsec²/pix), and then taking -2.5 log x, where x is the result of the conversion. To make the numbers more believable, and to imitate van der Kruit and Searle's original results, a constant (28) was added to each magnitude. The range of results fell between 20 and 25 magnitudes. These results were plotted separately for each radius, and then the results were displayed together in Fig. 5. A word about the error bars: the statistical error in each bin is assymetric when converted to magnitudes. This was not taken into account; instead, the lower error bar at each data point was made symmetric with the upper error bar. In reality, the lower error is somewhat less than depicted.

Figure 5. Set of z-profiles for NGC 4565. The vertical height (x-axis) is plotted against relative surface magnitude (y-axis) for ten different radii. Note that this is actually a collage of ten different vertical profiles at the same scale; the vertical height begins at 0 at each vertical profile. Radii are given in arcseconds and are measured from the edge of the frame. Visual inspection indicates that z₀ decreases as radius increases.

The final task was to establish the vertical scale height at each radius. This was done by attempting to fit the vertical profiles to the equation C sech² (z/z₀).
Without a computing algorithm to efficiently solve several systems of equations, the C constant was obtained by substituting 0 for the vertical height (sech² (0) = 1) and using the corresponding value at each radius to obtain C. This method assumes that the data around z=0 are accurate, a rather poor assumption considering the shapes of several of the above graphs. The z₀ parameter was then found by individually substituting the remaining values in the vertical profile and averaging the results. Two of the data points did not yield real solutions for z₀ by this method; they were discarded. The calculated values of z₀ are shown in Fig. 6. Linear regression analysis of the data indicates that the vertical scale height is indeed constant across the radius, as the slope of the line of best fit is very small:
Relative Magnitude = 32.98 - 0.0157R, where R is the radial distance from the edge of the frame. However, the correlation (-0.322) is not remarkable, which is likely due in large part to the crude fitting method used to find z₀.

Radius	No. of data points averaged	Mean z₀	Standard Deviation
56	10	38.4	5.5
91	4	32.9	3.2
126	2	24.0	0.1
161	4	28.2	2.7
196	4	30.6	6.1
231	4	25.2	5.2
266	4	35.5	3.0
301	4	23.0	2.7
336	3	26.2	2.8
371	2	32.3	4.6

Mean z₀: 29.6 arcsec

Figure 6. Mean z₀ for each of the vertical profiles examined.

Figure 7. Superimposition of all ten radial profiles indicating very little or no change in z₀ with respect to radius.

5. Discussion

To summarize, vertical profiles were obtained for 10 different radii of the edge-on spiral galaxy NGC 4565. These results were plotted and used to estimate the vertical scale height, which is shown to be approximately constant along the radius, but the correlation of the data to the line of best fit was unsatisfyingly low. Though not the focus of this research, it is not apparent from the profiles that the radial dependence of the luminosity (expressed as magnitudes) is nonlinear (Fig. 1). However, the graphs do seem to form a sech² function, and the inflection points are even visible in several of the profiles. While the aim of this study is not to gain new knowledge, this project is significant in a couple of ways. First, it successfully rediscovers van der Kruit and Searle's 20-year-old landmark results. Secondly, it demonstrates the capacities of the GOT and suggests new research.

Future studies in this direction should attempt to do absolute photometry with standard stars. Also, for long exposures, it is advisable to take separate blank sky fields rather than relying on blank sky in the object frames. Finally, since a great portion of a study's chance of success relies on the sophistication of the data analysis, familiarity with statistical methods and a few good software packages would be highly recommended.

References

van der Kruit, P.C. and Searle, L. 1981a, Astron. Astrophys., 95, 105.

Radial Dependence of the Vertical Scale Height in NGC 4565